A multiplicative model for efficiency analysis

This paper develops theory and algorithms for a “multiplicative” Data Envelopment Analysis (DEA) model employing virtual outputs and inputs as does the CCR ratio method for efficiency analysis. The frontier production function results here are of piecewise log-linear rather than piecewise linear form.     

Data envelopment analysis: The evolution of the state of the art (1978–1995)

The purpose of this paper is to briefly trace the evolution of DEA from the initial publication by Charnes et al. (1978b) to the current state of the art (SOA). The state of development of DEA is characterized at four points in time to provide a perspective in both directions—past and future. An evolution map is provided which illustrates DEA growth during the 17-year period, the timing of the major events, and the interconnections and influences between topics. An extensive DEA bibliography is provided.     

Some models and measures for evaluating performances with DEA: past accomplishments and future prospects

This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It starts with the “engineering-science” definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto–Koopmans definitions used in “welfare economics” as well as in the economic theory of production. Some of the models that have now been developed for implementing these concepts are then described and properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as “satisfactory” versus “full” (or “strong”) efficiency. They also include extensions from “efficiency” to “effectiveness” evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where “inputs” and “outputs” give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications in bringing further possibilities to the fore is highlighted.

Sensitivity and Stability Analysis in DEA: Some Recent Developments

This papersurveys recently developed analytical methods for studying thesensitivity of DEA results to variations in the data. The focusis on the stability of classification of DMUs (Decision MakingUnits) into efficient and inefficient performers. Early workon this topic concentrated on developing solution methods andalgorithms for conducting such analyses after it was noted thatstandard approaches for conducting sensitivity analyses in linearprogramming could not be used in DEA. However, some of the recentwork we cover has bypassed the need for such algorithms. Evolvingfrom early work that was confined to studying data variationsin only one input or output for only one DMU at a time, the newermethods described in this paper make it possible to determineranges within which all data may be varied for any DMU beforea reclassification from efficient to inefficient status (or vice versa) occurs. Other coverage involves recent extensionswhich include methods for determining ranges of data variationthat can be allowed when all data are varied simultaneously for all DMUs. An initial section delimits the topics to be covered.A final section suggests topics for further research.     

Sensitivity and Stability of the Classifications of Returns to Scale in Data Envelopment Analysis

Sensitivity of the returns to scale (RTS) classifications in data envelopment analysis is studied by means of linear programming problems. The stability region for an observation preserving its current RTS classification (constant, increasing or decreasing returns to scale) can be easily investigated by the optimal values to a set of particular DEA-type formulations. Necessary and sufficient conditions are determined for preserving the RTS classifications when input or output data perturbations are non-proportional. It is shown that the sensitivity analysis method under proportional data perturbations can also be used to estimate the RTS classifications and discover the identical RTS regions yielded by the input-based and the output-based DEA methods. Thus, our approach provides information on both the RTS classifications and the stability of the classifications. This sensitivity analysis method can easily be applied via existing DEA codes.